A curve is such that \(\frac{d^2y}{dx^2}=(2x+3)^{-1/2}\). The curve has a gradient of \(5\) at the point where \(x=3\), and passes through the point \(\left(\frac12,-\frac13\right)\).

(i) Find the equation of the curve.

(ii) Find the equation of the normal to the curve at the point where \(x=3\), giving your answer in the form \(ax+by+c=0\), where \(a\), \(b\) and \(c\) are integers.